] I think the Popes were handing out lots and lots of papal dispensations to the royals. But then again, since they were busy keeping their mistresses and children in line, they were probably weren't too concerned about a little mixed blood. A little gold always does wonders!

I'm no expert either, but my Dad is, and papal dispensations went with a hefty fee (or donation :)) so it was possibly a large income source for the Vatican. I know of one case in the 16th century when the pope gave special dispensation for a full brother and sister to marry! It was a politically and financially advantageous match for the family and the Church. So if you are rich and powerful enough, you can always move mountains!